1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
exis [7]
3 years ago
15

Is 3.734795.... a rational or irrational number? and why

Mathematics
1 answer:
Marina CMI [18]3 years ago
7 0

Answer:

Let's look at what makes a number rational or irrational ...

Rational Numbers

A Rational Number can be written as a Ratio of two integers (ie a simple fraction).

Example: 1.5 is rational, because it can be written as the ratio 3/2

Example: 7 is rational, because it can be written as the ratio 7/1

Example 0.333... (3 repeating) is also rational, because it can be written as the ratio 1/3

 

Irrational Numbers

But some numbers cannot be written as a ratio of two integers ...

...they are called Irrational Numbers.

Example: π (Pi) is a famous irrational number.

Pi

π = 3.1415926535897932384626433832795... (and more)

We cannot write down a simple fraction that equals Pi.

The popular approximation of 22/7 = 3.1428571428571... is close but not accurate.

Another clue is that the decimal goes on forever without repeating.

Cannot Be Written as a Fraction

It is irrational because it cannot be written as a ratio (or fraction),

not because it is crazy!

So we can tell if it is Rational or Irrational by trying to write the number as a simple fraction.

Example: 9.5 can be written as a simple fraction like this:

9.5 =  

19

2

 

So it is a rational number (and so is not irrational)

Here are some more examples:

Number   As a Fraction   Rational or

Irrational?

1.75    

7

4

   Rational

.001    

1

1000

   Rational

√2

(square root of 2)   ?   Irrational !

Square Root of 2

Let's look at the square root of 2 more closely.

square root 2 When we draw a square of size "1",

what is the distance across the diagonal?

The answer is the square root of 2, which is 1.4142135623730950...(etc)

But it is not a number like 3, or five-thirds, or anything like that ...

... in fact we cannot write the square root of 2 using a ratio of two numbers

... I explain why on the Is It Irrational? page,

... and so we know it is an irrational number

Famous Irrational Numbers

Pi    

Pi is a famous irrational number. People have calculated Pi to over a quadrillion decimal places and still there is no pattern. The first few digits look like this:

3.1415926535897932384626433832795 (and more ...)

e (eulers number)    

The number e (Euler's Number) is another famous irrational number. People have also calculated e to lots of decimal places without any pattern showing. The first few digits look like this:

2.7182818284590452353602874713527 (and more ...)

phi    

The Golden Ratio is an irrational number. The first few digits look like this:

1.61803398874989484820... (and more ...)

radical symbol    

Many square roots, cube roots, etc are also irrational numbers. Examples:

√3 1.7320508075688772935274463415059 (etc)

√99 9.9498743710661995473447982100121 (etc)

But √4 = 2 (rational), and √9 = 3 (rational) ...

... so not all roots are irrational.

pls, branliest :)

You might be interested in
I WILL GIVE A BRANLIEST!<br>What is the graph of the functions?<br> y=2*2^x<br> y=-2*5^x
tekilochka [14]
For this case what you should know is that both functions are of the potential type.
 We have then that
 y = 2 * 2 ^ x
 This function grows exponentially upwards.
 y = -2 * 5 ^ x
 This function grows exponentially downwards.
 Answer
 See attached graphics.

4 0
2 years ago
It took emily 25 min to rideHer bicycle to the repair shop in one hour and 15 minutes to walk back home. If Emily her bicycle to
s2008m [1.1K]

Answer:the repair shop is 5km from her house.

Step-by-step explanation:

Let x represent the distance of the repair shop from her house.

Let y represent Emily's speed when riding.

Distance = speed × time

It took Emily 25 min to ride her bike to the repair shop. Converting 25 min to hours, it becomes 25/60 = 5/12 hours.

Distance covered,

x = y × 5/12 = 5y/12

It took her 1h 15 min to walk back home. Converting to hours, it becomes 1 + 15/60 = 1 1/4 = 5/4

If she can ride her bike 8km/h faster than she can walk, it means that her speed while walking would be y 8 8

Therefore,

Distance covered,

x= 5/4(y - 8) = (5y - 40)/4

Since the distance remains the same, then

5y/12 =(5y - 40)/4

Crossmultiplying, it becomes

5y × 4 = 12(5y - 40)

20y = 60y - 480

60y - 20y = 480

40y = 480

y = 480/40 = 12

x = 5y/12 = 5 × 12/12 = 5 km

6 0
2 years ago
In class A, John got 85 for his first test John's class mean was 75 and standard deviation was 5. In class B, Kathy got 80 in he
ivanzaharov [21]

Answer:

b. Kathy

Step-by-step explanation:

We compare each of their score by how far away from the mean when in term of the standard deviation. Using the following formula

\frac{x - \mu}{\sigma}

For John he is (85 - 75)/5 = 2.

For Kathy she is (80 - 50)/10 = 3.

Since Kathy is 3 standard deviation better than her class' average, while John is only 2's. We conclude that Kathy did better.

6 0
2 years ago
In the given figure, identify a pair of perpendicular lines.
irakobra [83]
The answer is m and n / c
5 0
2 years ago
Read 2 more answers
How are numbers related?
MAVERICK [17]
<span> <span>two numbers are related in this way:
the number 1 is subtracted from the first number, the difference is squared, then doubled;the result is equal to the second number. the number 1 is added to the first number, and the sum is squared;the result is equal to 4 minus the second number. determine the numbers. </span></span>
3 0
3 years ago
Other questions:
  • Consider the infinite geometric series ∑∞n=1−4(13)n−1
    15·2 answers
  • Molli purchased 8 apples for $4.25.
    9·1 answer
  • Obasi earns 150%, percent of his regular hourly wage while working overtime. What fraction of his regular hourly wage does Obasi
    15·2 answers
  • What is the volume of a pyramid with a base of 22 and a height of 24
    10·1 answer
  • Sally needs 2 1/4 cups of flour to make her cake. She has 1 3/8 cups of flour. How much flour will she need to borrow to have en
    14·2 answers
  • How many solutions does this system have?
    14·2 answers
  • Please Help!!!<br> Due: Monday<br> On Ellipses - Pre Calc
    11·1 answer
  • If f(x)=x+8 and g(x)=-4x-3 find (f+g)(x)
    9·1 answer
  • HELPPPPPPPPPPPPPPPPPPPPPPPP
    6·2 answers
  • Which choice below lists all of the square roots of the number 15?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!